相关论文: Observability and unique continuation of the adjoi…

The class of port-Hamiltonian systems incorporates many physical models, such as mechanical systems in the finite-dimensional case and wave and beam equations in the infinite-dimensional case. In this paper we study a subclass of linear…

In this short note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove nonuniqueness of admissible weak solutions that start…

We consider the time dependent Euler--Bernoulli beam equation with discontinuous and singular coefficients. Using an extension of the H\"ormander product of distributions with non-intersecting singular supports [L. H\"ormander, The Analysis…

We implement molecular dynamics simulations in canonical ensemble to study the effect of confinement on a $2d$ crystal of point particles interacting with an inverse power law potential proportional to $r^{-12}$ in a narrow channel. This…

In this paper, we investigate the long-time dynamics of the linearized 2-D Euler equations around a hyperbolic tangent flow $(\tanh y,0)$. A key difference compared to previous results is that the linearized operator has an embedding…

We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…

Nonequilibrium transport measurements in mesoscopic quasi-ballistic 2D electron systems show an enhancement in the differential conductance around the Fermi energy. At very low temperatures, such a zero-bias anomaly splits, leading to a…

The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations,…

Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The…

We investigate non-equilibrium lane formation in a generic model of a fluid with attractive interactions, that is, a two-dimensional Lennard-Jones (LJ) fluid composed of two particle species driven in opposite directions. Performing…

Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…

In the present paper, we study the existence, uniqueness and behaviour in time of the solutions to the Darcy-B\'enard problem for an extended-quasi-thermal-incompressible fluid-saturated porous medium uniformly heated from below. Unlike the…

This paper addresses the analysis of a boundary feedback system involving a non-homogeneous Euler-Bernoulli beam governed by the equation $m(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the initial $u(x,0)=u_0(x)$,…

We consider a 2D infinite channel domain with an incompressible fluid satisfying the so-called dynamic slip boundary condition on the (part of the) boundary. Introducing an exhaustion by a sequence of bounded sub-domains of the whole…

The response of inviscid incompressible unbounded fluid subject to a localized external perturbation is studed. The physically relevant hypotheses on the mode coupling mechanisma is justified by renormalization group method. The scaling…

This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of…

A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…

This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of…

We study the linear Zakharov--Kuznetsov equation with periodic boundary conditions. Employing some tools from the nonharmonic Fourier series we obtain several internal observability theorems. Then we prove various exact controllability and…

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using…